A. Overview
A Sagnac interferometer comprises a splitting plate or other splitting device that divides an incident light wave into two lightwaves. The two waves thus created enter opposite ends of a single optical path formed into a loop. The two waves counter-propagate, pass through each other, and return to the splitting device. There they recombine and are sent to a detector where they produce interference that depends upon phase difference between the recombined waves.
Originally, mirrors defined the optical path of the Sagnac interferometers. It is now known that this optical path can be created using a single-mode optical fiber wound about an axis into a coil.
It is also known that rotating the coil about its axis changes the relative optical path lengths of the counter-propagating waves, engendering a phase difference between these waves when they recombine. The recombination of the two counter-propagated waves creates interference between them that is modified by their phase difference and thereby the rate of rotation of the fiber coil. This is known as the Sagnac effect. The measurement of this phase difference enables the rotation rate to be quantified.
Much work has been conducted in order to improve the sensitivity and accuracy of the rotation rate measurement performed with such a gyroscope. As regards this topic, it will for example be possible to consult the books “The Fiber-Optic Gyroscope” by Herve Lefevre, ARTECH HOUSE, 1992, and “Optical Fiber Rotation Sensing” edited by William K. Burns, ACADEMIC PRESS, 1993.
In particular, it has firstly been observed that the response furnished by the SAGNAC interferometer in its simplest form is P(Δφ)=P0[1+cos(Δφ)] and hence that the sensitivity of this signal of detected optical power, P(Δφ), in the neighborhood of the phase difference Δφ=0, is low. A graph of P(Δφ) versus Δφ is known as an interferogram. The sensitivity is also low near phase differences that are integer multiples of pi radians. A square wave phase difference modulation, with amplitude more or less pi/2 has been used to displace the operating point and produce a periodic signal the amplitude of which, S(Δφ), is a sinusoidal function of the rotation rate, S(Δφ)=S0[sin(Δφ)], and which can hence be exploited with greater sensitivity and stability near phase differences of zero, Δφ=0, or integer multiples of pi radians.
It was later shown that the accuracy of the measurement is improved by the use of a zero method, also called closed-loop operation. According to this method, an additional so-called negative-feedback phase difference ΔφmR is applied, and serves to compensate for phase difference ΔφR produced by the rotation rate. The sum of these two phase-differences, ΔφmR and ΔφR, is kept null, thus enabling the interferometer to be operated with maximum sensitivity over a wide range of rotation rates. The signal necessary for producing the negative-feedback phase difference ΔφmR is then exploited to derive a measurement of rotation rate. The measurement is then stable and linear.
The slaving necessary for this closed-loop operation can be performed through a frequency offset as was done using acousto-optic modulators in U.S. Pat. No. 4,299,490. Use of a pure frequency-shifting device, such as the acousto-optic modulators, is simple in principle, but difficult in practice.
The difficulty in implementing the frequency shifter approach led to reconsideration of closing the loop using a phase modulator. A constant frequency offset is equivalent to a constant rate-of-change in phase, or, in other words, a ramp in phase vs. time with a constant slope. A phase modulator can generate a phase ramp for a short period of time, but it then reaches the limit of its capability. An instantaneous 2π shift in the phase is transparent to an optical wave, and therefore a serrodyne waveform, consisting of a ramp and fall-back, created by a phase modulator appears like a continuous phase ramp and therefore also like a frequency shift.
A problem with phase modulators is that each phase modulator produces a slightly different phase modulation for a given electronic drive signal. Furthermore, the amount of phase modulation changes depending upon the temperature. This leads to an inadequate knowledge of the phase shifts that are imparted to the counter-propagating waves, and manifests itself in an inadequate knowledge of the phase shift used to compensate for the Sagnac phase difference and a less than accurate 2pi fall-back. To make an accurate determination of the phase shift, a second control loop is required.
The aforesaid second control loop has been implemented in different ways. All of these have in effect rendered the actual ratio of the phase modulation output to electronic input, i.e. the phase modulator transfer function, non-critical to the measurement of Sagnac phase difference. The second control loop calibrates the phase modulator transfer function against the response of the interferometer. If the second control loop works well, then the measurement becomes as good as the interferometer response, and therefore as good as fundamental parameters such as wavelength stability and fiber coil stability.
In the serrodyne approach, the signal following the fall back is used as the input to the second control loop. This signal indicates an error if the fall back differs from 2pi radians, and thus it calibrates the phase modulator transfer function with respect to the optical signal.
In order to simplify the electronic hardware, and reduce cost, the detector output is digitized, signal processed, and converted back into an analog waveform to drive the phase modulator. The electronic signal processing may comprise a combination of analog signal-conditioning electronics, conversion electronics, and digital electronics. With this arrangement it is easier to change the level of the electronic drive waveform in discrete steps rather than continuously. In a Sagnac loop interferometer, phase modulation steps can provide a similar phase difference between the recombined counter-propagated waves as a continuous ramp. The continuous ramp and fall-back then becomes a series of steps and a fall-back. See, for example, U.S. Pat. Nos. 5,039,220, 5,141,316, 5,181,078.
An alternative approach is called dualramp feedback and it uses two phase ramps to shift the phase difference back and forth from pi radians to minus pi radians as described in U.S. Pat. No. 4,869,592. This approach has been implemented using largely analog electronics and two control loops, one for the plus pi phase difference and one for the minus pi phase difference. The staircase form of this phase modulation method amounts to taking two or more steps in each direction, i.e. up and down, some times referred to as “dual staircase modulation”. The dual staircase modulation is distinguished from the staircase-and-fall-back method because the former takes two or more steps in each direction while the latter uses only a single step in the opposite direction of the staircase to keep the phase modulator and electronics within their ranges of operation. Illustrated in U.S. Pat. No. 6,744,519 is a version of the dual staircase modulation waveform.
The dual-staircase feedback is better than the continuous ramp up and ramp down, not only because of better compatibility with digital electronics, but also because the dual-staircase approach has a much shorter switching time between plus pi phase difference and minus pi phase difference relative to the dual-ramp approach. The switching time changes a couple of orders of magnitude from the order of microseconds, approximately the propagation time through the fiber loop, to a few nanoseconds, the rise time of the phase step.
B. Basic Fiber Gyroscope Design
The fiber-optic gyroscope, see FIG. 1, includes a quasi-monochromatic light source 15, that is most often a super-luminescent diode or a laser diode pumped erbium-doped optical fiber, and a single-mode fiber optic Sagnac loop interferometer, designated overall by the reference 10. The Sagnac loop interferometer 10 comprises a first beam splitter 19 and an optical path 20 constituted by a single-mode optical fiber wound into a coil. The incident light wave is divided into two waves by the beam splitter. The two waves thus created are fed into opposite ends of the optical fiber and propagate in opposite directions, or counter-propagate, through the fiber. The counter-propagating waves pass through each other and return to the beam splitter where they are each split again thereby creating four waves. Two of these four waves, a portion from each of the counter-propagated waves, combine with each other and return in the direction of the source of the incident wave while the other two combine with each other but exit the interferometer through the unused port of the first beam splitter 19 and are discarded.
This gyroscope likewise comprises a detector 11 furnishing an electrical signal that is proportional to the optical power incident upon it. The optical power is a function of phase difference between the combined counter-propagated waves. In other words, the combined waves interfere with each other and the amount of the optical power at the detector is a function of the state of this interference. A graph of the detected optical power vs. total phase difference between the interfering waves is known as the interferogram, see FIG. 2, and also FIGS. 10c, 11b and 12b. The optical signal is furnished to the detector 11 via a second beam splitter 16 that can be constituted, for example, by a semi-transparent mirror.
In the optical path of the interferometer there is interposed a modulator 14 that, controlled on the basis of an electrical signal, imparts a phase shift φm(t) to both of the counter-propagating waves. The difference in the propagation time from the phase modulator to the detector in one direction around the loop versus the other is τ, and therefore a modulation of φm(t) applied to both waves at the phase modulator 14 creates a phase difference Δφm(t)=φm(t)−φm(t−τ) between the two waves at the detector 11. Phase modulation, φm(t), is distinguished from phase difference modulation, Δφm(t), in the discussion that follows. Phase modulation, φm(t), is added to the phase of each of the counter-propagating waves at the phase modulator 14. Phase difference modulation, Δφm(t), is the modulation of the difference between the phases of the two waves as they interfere with each other at the detector 11. The detected optical power is largely dependent upon the total phase difference, ΔφT(t), between the interfering waves. The total phase difference is ideally the sum of the modulated phase difference plus the rotation-rate induced phase difference.
The operation of the interferometer is improved by interposing a polarizer 17 and a spatial filter 18 between the second beam splitter 16 and the first beam splitter 19. In a known manner, this spatial filter is constituted by a single-mode optical fiber. Light returning from the interferometer 10 must have a component of its polarization aligned with pass axis of the polarizer 17. Employing polarization-maintaining fiber with its axes of birefringence properly aligned will ensure that some light is passed by the polarizer 17 and delivered to the detector 11. If the pass axis of the polarizer 17 is vertical, and the slow axis of each of the fiber ends is vertical, and the first beam splitter 19 is relatively insensitive to the polarization of the light, or its birefringence axis is similarly aligned, then a large amount of the light returning to the polarizer 17 will pass through to the second beam splitter 16 and on to the detector 11.
The output of the detector 11 is prepared and digitized with an analog-to-digital converter 12. The proper signal preparation necessary to avoid excess errors in the digital conversion is described in the next subsection. Closed-loop signal processing and digital-to-analog conversion electronics, herein referred to as signal processor 13, provides negative feedback to control the phase modulator 14 as a function of the signal received from the detector 11. It also creates the bias modulation that is added to the feedback modulation. Finally it derives the rotation rate measurement value that is output for external use.
C. Analog-To-Digital Conversion
A block diagram of analog-to-digital conversion electronics 12 of FIG. 1 is shown in FIG. 3. The output of the detector 11 passes through an amplifier 21 and a low-pass filter 22 before reaching the analog-to digital converter (ADC) 23. Analog-to-digital conversion changes an electronic signal and electronic noise that accompanies the signal, but this change can be made to have almost negligible impact in the signal-to-noise ratio if three criteria are met. The first criterion is that the noise accompanying the analog signal must have a standard deviation that is larger than about one least significant bit (LSB) of the ADC 23. The amplifier 21 is used to increase both signal and noise that is output from the detector 11 to satisfy the first criterion. The second criterion is that the dynamic range of the signal and noise are smaller that the dynamic range of the ADC 23. Thus the amplifier is not allowed to over-amplify the signal and noise, and the ADC must have enough bits to measure the signal plus noise. The third criterion is that the low-pass filter 22 must attenuate the analog frequency components that are approximately equal to or greater than the sampling frequency of the ADC 23. These components are undesirable because high frequency analog noise can alias to low frequency digital noise by the digitization process.
Satisfying the above stated criteria renders sampling noise negligible relative to noise present in the analog signal. Moreover, additional digital filtering leads in this case to the same improvement in the signal-to-noise ratio as filtering would accomplish in analog mode. As a practical example, the sampling period is 1/16 times the propagation time τ, namely, for example τ=5 microseconds for 1000 meters of fiber, and the sampling period is 0.31 microseconds. The Shannon criterion therefore imposes a large pass band on the signal to be sampled: it has to be equal to 1/(2 times the sampling period), namely 1.6 MHz in this example. In such a pass band the noise is relatively large: typically a standard deviation of 10−3 of the detected optical power, which corresponds to a phase shift of about 10−3 radians in the interferometer. Hence it is sufficient, in order not to lose sensitivity and in order to be able later to improve the signal to noise ratio by filtering, that the LSB correspond to this phase shift.
For its part, the high limit must be at least greater than the peak-to-peak value of the noise, namely about 8 times its standard deviation and hence 3 bits would suffice for sampling the noise alone. However, account must also be taken of the inherent variations in the signal: in closed-loop mode the latter is slaved to zero and would not therefore a priori lay claim to any variations but in practice the slaving deviates from zero during changes in the rotation rate, i.e. angular acceleration, and the dynamic range of the converter must be able to cope with these deviations. These variations therefore define the number of necessary bits. In practice 8 to 12 bits are sufficient at the converter level, whilst after digital filtering the dynamic range of the rotation rate measurement can be greater than 20 bits.
D. Closed-Loop Signal Processing and Digital-To-Analog Conversion Electronics
Closed loop signal processing block diagrams as well as digital-to-analog conversion electronics take different forms depending upon the loop closure approach. Two approaches are reviewed: first the staircase-and-fall-back approach and second the dual staircase approach. Each of these two approaches uses two control loops, but they have quite different configurations.
The staircase-and-fall-back approach described here has a first control loop to null the Sagnac phase difference and a second control loop to control the gain of the digital-to-analog conversion and phase modulation portions of the first control loop. I will refer to the first control loop of this approach as the rotation-rate control loop because it is responsive to the rotation rate. I will refer to the second control loop as the calibration control loop because it calibrates the digital values in the signal processing against the phase modulation of the optical wave.
The prior-art dual staircase approach also has two control loops, a first control loop to control the height of the up-steps to shift the total phase difference to plus pi radians and a second to control the down steps to shift the total phase difference to minus pi radians. When the gyroscope is rotating, the up-step height is not the same as the down-step height. Therefore there is a difference between the number of up steps and the number of down steps and this difference is used as a measure of rotation. The rotation rate measurement in both the dual-staircase approach and the staircase-and-fall-back approach is largely independent of the phase modulator transfer function.
The signals involved in the above-mentioned control loops share the same path through most of the gyroscope. Their paths differ only within the closed loop signal processing and the digital-to-analog conversion electronics. To trace the common paths we can begin at the phase modulator 14, progress through the optics, through the detector 11, and through the analog-to-digital conversion electronics 12. The latter comprises the amplifier 21, the low-pass filter 22, and the ADC 23. The completion of the individual paths through the signal processing and through the digital-to-analog conversion electronics is discussed below.
1. Staircase-And-Fall-Back Signal Processing Block Diagram and Corresponding Waveform
Block 13 of FIG. 1 is shown in more detailed block diagram form for the staircase-and-fall-back approach in FIG. 4. To become familiar with this block diagram we trace the paths of the feedback signals from block to block to complete the control loops discussed above. We will then show where the bias modulation is introduced and afterwards discuss the operation of the loops.
The first control loop, i.e. the rotation-rate loop, is completed by sending the signal from ADC 23 through a rotation-rate processor 44, a feedback accumulator 46, through an adder 52, a multiplying DAC 55 and an amplifier 32 before returning to the phase modulator 14. Completion of the second control loop, i.e. the calibration control loop, from ADC 23 to phase modulator 14 is by way of a calibration processor 45, DAC 56, multiplying DAC 55, and amplifier 32.
A digital version of the bias waveform is generated in a bias waveform generator 53, added to the feedback waveform in an adder 52. Its amplitude is adjusted in the multiplying DAC 55 and is amplified in amplifier 32 and sent to phase modulator 14. The bias modulation causes the rotation-rate signal entering the rotation-rate processor 44 to be modulated at the bias modulation frequency. Demodulation at the bias modulation frequency returns the rotation-rate signal to the same frequency as the actual rotation rate. For example, a constant rotation rate of the gyroscope would yield a DC, i.e. constant, rotation-rate signal after demodulation.
The input to the rotation rate processor 44 is the digitized detector signal and the output of the rotation-rate processor 44 is a digital value corresponding to the rotation rate. The rotation rate digital value in this approach is the desired output and is delivered directly to the measurement output 41.
The input of the calibration signal processor 45 is the same as the input of the rotation-rate signal processor 44. The demodulation in the calibration signal processor 45 is, however, quite different. For calibration purposes the important part of the input signal occurs in relation to the fall back of the feedback signal, and thus calibration demodulation frequency is the same as the staircase-and-fall-back frequency. The demodulation reference signal comes directly from the feedback waveform generator 30. The output of the calibration signal processor 45 is a pi digital value corresponding to a predetermined optical phase difference. The DAC 56 converts the pi digital value to a calibration analog signal, and that calibration analog signal becomes the reference signal to the multiplying DAC 55. As the multiplying DAC 55 reference signal, the calibration analog signal adjusts the gain of the multiplying DAC 55 for the feedback waveform coming from the feedback accumulator 46 through adder 52 and going to amplifier 32. The gain is adjusted to keep the total gain from the output of the feedback waveform accumulator 46 to the actual phase modulation imparted to the optical waves constant.
An example of the staircase-and-fall-back phase modulation for the above electronics is shown in FIG. 5. FIG. 5a shows a staircase with a step width of τ seconds, approximately the propagation time of light around the fiber loop. Each step height on FIG. 5a is equal to ΔφmR=π/6, to compensate for a Sagnac phase shift of ΔφR=−π/6 due to rotation rate. The overflow of the accumulator creates the fall back or a step down of 2π−ΔφmR=11π/6. The bias modulation φmb(t) shown in FIG. 5b is added to the staircase-and-fall-back feedback modulation φmfs(t) to complete the phase modulation φms(t) shown in FIG. 5c. The phase modulation is repeated in FIG. 5d along with the phase modulation φms(t−τ) of the other counter-propagating wave (dotted line) that took the long way from phase modulator to detector and is delayed by τ. The difference of the two waveforms in FIG. 5d is the phase difference modulation Δφms(t)=φms(t)−φms(t−τ) and it is shown in FIG. 5e. The phase difference is a square wave with the exception of a 2pi-shifted portion due to the fall-backs. The short-term average not including the 2pi-shifted portions is displaced from zero to compensate for the Sagnac phase difference, but the long-term average including the 2pi-shifted portions is precisely zero.
2. Dual-Staircase Waveform and Corresponding Closed-Loop Signal Processing Block Diagram
The prior-art version of the dual-staircase modulation for the same Sagnac phase shift of ΔφR=−π/6 is shown in FIG. 6. The up steps have a different height from the down steps, see FIG. 6a, because the phase difference must be shifted from ΔφR=−π/6 to plus pi during the up steps and to minus pi during the down steps. Specifically, the up steps have a step height of 7π/6 to shift the phase difference from −π/6 to +π and the down steps have a step height of 5π/6 τo shift the phase difference from −π/6 to −π. Note that it is necessary to have more down steps than up steps to keep the phase modulation within the range of the phase modulator. The bias modulation φmb(t), shown in FIG. 6b, is added to the feedback modulation φmfdspa(t) to create the total phase modulation φmdspa(t) of FIG. 6c. The resulting phase difference modulation Δφmdspa(t) is shown in FIG. 6d. Note that the phase difference modulation Δφmdspa(t) is offset by π/6 to compensate for the Sagnac phase difference ΔφR(t) of −π/6.
Block 13 of FIG. 1 is shown in more detailed block diagram form for the dual-staircase approach in FIG. 7. To become familiar with this block diagram we trace the paths of the feedback signals from block to block to complete the control loops from the ADC 23 to the phase modulator 14. In this prior art version of the dual-staircase approach one of the two control loops controls the height of the up steps of the above-mentioned modulation waveform, and the other controls the height of the down steps. We will then show where the bias modulation is introduced and afterwards discuss the remaining blocks of the diagram.
As part of both control loops a demodulator 48 receives the digitized signal from the ADC 23. The output of the demodulator 48 then feeds the up-step accumulator 49 after each up-step and the down-step accumulator 50 after each down step. A multiplexor 51 brings the loops back together again by switching the outputs of either the up-step accumulator 49 or the down-step accumulator 50 to a feedback accumulator 30 depending upon whether up-steps or down-steps are required to keep the output of the feedback accumulator 30 within a specified range. The feedback accumulator 30 outputs a series of digital values corresponding to the feedback modulation waveform, see, for example, FIG. 6a. This feedback modulation waveform is added to the bias modulation waveform, see FIG. 6b, output from the bias waveform generator 53, in an adder 52 The DAC 31 receives the signal from the adder 52, converts it to an analog signal and delivers it to an amplifier 32 that in turn drives the phase modulator 14.
Limits of the feedback accumulator 30 are preset in a limit detector 31. The limit detector receives the output of the feedback accumulator 30 and compares it against these limits and outputs a signal to the multiplexor 51 that selects which of either the down-step-accumulator 50 output or the up-step-accumulator 49 output will be delivered to the input of the feedback accumulator 30. The output of the limit detector 31 also drives the input of an up/down counter 54. The up/down counter 54 adds one to its output for every up step and subtracts one from its output for every down step. The output of the up/down counter 54 is a measure of the rotation rate and it is delivered to the measurement output 41 for external use.
A digital version of the bias waveform is generated in a bias waveform generator 53, added to the feedback waveform in an adder 52. The sum of the bias modulation and the feedback modulation is converted to an analog signal by the DAC 31 and is amplified in amplifier 32 and sent to phase modulator 14. The bias modulation causes the rotation-rate signal entering the demodulator 48 to be modulated at the bias modulation frequency. Demodulation at the bias modulation frequency returns the rotation rate signal to the same frequency as the actual rotation rate.